Elementary technical mathematics

1.1 Review of Basic Operations 21.2 Order of Operations 111.3 Area and Volume 141.4 Formulas 191.5 Prime Factorization Divisibility 23Unit 1A: Review 27 Unit 1B REVIEW OF OPERATIONS WITH

Trang 2

Elementary Technical Mathematics

Trang 3

Printed in the United States of America

1 2 3 4 5 6 7 13 12 11 10 09

Math Editor: Marc Bove

Assistant Editor: Stefanie Beeck

Editorial Assistant: Kyle O’Loughlin

Media Editor: Heleny Wong

Marketing Manager: Ashley Pickering

Marketing Assistant: Angela Kim

Marketing Communications Manager:

Mary Anne Payumo

Content Project Manager: Jerilyn Emori

Creative Director: Rob Hugel

Art Director: Vernon Boes

Print Buyer: Linda Hsu

Rights Acquisitions Account Manager, Text:

Bob Kauser

Rights Acquisitions Account Manager,

Image: Don Schlotman

Production Service: Lynn Steines,

S4Carlisle Publishing Services

Text and Cover Designer: Roy Neuhaus

Photo Researcher: Jennifer Lim, Bill Smith

Group

Copy Editor: Lorretta Palagi

Cover Image: Clockwise, from top: David

Joel/Getty Images, Mark Richards/

PhotoEdit, Monty Rakusen/Getty

Images, Jupiterimages/Getty Images,

David Young-Wolff/PhotoEdit,

Thinkstock Images/Getty Images,

Stockbyte/Getty Images

Compositor: S4Carlisle Publishing Services

herein may be reproduced, transmitted, stored, or used in any form or

by any means graphic, electronic, or mechanical, including but not ited to photocopying, recording, scanning, digitizing, taping, web distribution, information networks, or information storage and retrieval systems, except as permitted under Section 107 or 108 of the 1976 United States Copyright Act, without the prior written permission of the publisher.

lim-For product information and technology assistance, contact us at C

Ce engage e L Learrn niin ng g C Cu usstto om me err & & S Sa alle ess S Supporrtt,, 11 8 800 33554 4 9 9770 06 6 For permission to use material from this text or product, submit all requests online at w www cce engage e cco om m//p pe errm miissssiio on nss

Further permissions questions can be e-mailed to p

pe errm miissssiio on nrre eque esstt@ @cce engage e cco om m

Library of Congress Control Number: 2009923966 Student Edition:

ISBN-13: 978 439046890 ISBN-10: 1-4390-4689-1 B

Brro oo ok kss//C Co olle e

10 Davis Drive Belmont, CA 94002-3098 USA

Cengage Learning is a leading provider of customized learning solutions with office locations around the globe, including Singapore, the United Kingdom, Australia, Mexico, Brazil, and Japan Locate your local office at w

www cce engage e cco om m//g gllo ob ba Cengage Learning products are represented in Canada by Nelson Education, Ltd.

To learn more about Wadsworth, visit w ww ww w cce engage e cco om m//b brro oo ok ksscco olle e Purchase any of our products at your local college store or at our preferred online store w ww ww w iicch haptte errss cco om m

1

Trang 4

1.1 Review of Basic Operations 21.2 Order of Operations 111.3 Area and Volume 141.4 Formulas 191.5 Prime Factorization Divisibility 23

Unit 1A: Review 27 Unit 1B

REVIEW OF OPERATIONS WITH FRACTIONS 27

1.6 Introduction to Fractions 271.7 Addition and Subtraction of Fractions 331.8 Multiplication and Division of Fractions 451.9 The U.S System of Weights and Measures 53

Unit 1B: Review 56 Unit 1C

REVIEW OF OPERATIONS WITH DECIMAL FRACTIONS AND PERCENT 57

1.10 Addition and Subtraction of Decimal Fractions 571.11 Rounding Numbers 66

1.12 Multiplication and Division of Decimal Fractions 691.13 Percent 75

1.14 Rate, Base, and Part 801.15 Powers and Roots 891.16 Applications Involving Percent: Personal Finance (Optional) 93

Unit 1C: Review 97 Chapter 1: Group Activities 98 Chapter 1: Summary 99 Chapter 1: Review 102 Chapter 1: Test 104

1

Trang 5

3

4

2.1 Addition of Signed Numbers 1082.2 Subtraction of Signed Numbers 1122.3 Multiplication and Division of Signed Numbers 1142.4 Signed Fractions 117

2.5 Powers of 10 1222.6 Scientific Notation 1252.7 Engineering Notation 131

Chapter 2: Group Activities 134 Chapter 2: Summary 134 Chapter 2: Review 136 Chapter 2: Test 137 Chapter 1-2: Cumulative Review 138

3.1 Introduction to the Metric System 1403.2 Length 143

3.3 Mass and Weight 1463.4 Volume and Area 1483.5 Time, Current, and Other Units 1523.6 Temperature 154

3.7 Metric and U.S Conversion 156

Chapter 3: Group Activities 161 Chapter 3: Summary 161 Chapter 3: Review 162 Chapter 3: Test 163

4.1 Approximate Numbers and Accuracy 1664.2 Precision and Greatest Possible Error 1694.3 The Vernier Caliper 173

4.4 The Micrometer Caliper 1814.5 Addition and Subtraction of Measurements 1894.6 Multiplication and Division of Measurements 1934.7 Relative Error and Percent of Error 196

4.8 Color Code of Electrical Resistors 2004.9 Reading Scales 204

Trang 6

5.5 Multiplication of Polynomials 2325.6 Division by a Monomial 2345.7 Division by a Polynomial 236

6.1 Equations 2446.2 Equations with Variables in Both Members 2496.3 Equations with Parentheses 251

6.4 Equations with Fractions 2546.5 Translating Words into Algebraic Symbols 2596.6 Applications Involving Equations 260

6.7 Formulas 2656.8 Substituting Data into Formulas 2686.9 Reciprocal Formulas Using a Calculator 272

7.1 Ratio 2807.2 Proportion 2847.3 Direct Variation 2907.4 Inverse Variation 295

Trang 7

Graphing Linear Equations 303

8.1 Linear Equations with Two Variables 3048.2 Graphing Linear Equations 310

8.3 The Slope of a Line 3178.4 The Equation of a Line 323

9.1 Solving Pairs of Linear Equations by Graphing 3349.2 Solving Pairs of Linear Equations by Addition 3409.3 Solving Pairs of Linear Equations by Substitution 3459.4 Applications Involving Pairs of Linear Equations 347

10.1 Finding Monomial Factors 35810.2 Finding the Product of Two Binomials Mentally 36010.3 Finding Binomial Factors 362

10.4 Special Products 36510.5 Finding Factors of Special Products 36710.6 Factoring General Trinomials 369

8

9

10

11

Trang 8

Contents vii

12.1 Angles and Polygons 39812.2 Quadrilaterals 40512.3 Triangles 41012.4 Similar Polygons 41912.5 Circles 423

12.6 Radian Measure 43012.7 Prisms 435

12.8 Cylinders 44112.9 Pyramids and Cones 44612.10 Spheres 453

13.1 Trigonometric Ratios 46613.2 Using Trigonometric Ratios to Find Angles 47013.3 Using Trigonometric Ratios to Find Sides 47313.4 Solving Right Triangles 474

13.5 Applications Involving Trigonometric Ratios 476

14.1 Sine and Cosine Graphs 49014.2 Period and Phase Shift 49614.3 Solving Oblique Triangles: Law of Sines 50014.4 Law of Sines: The Ambiguous Case 50314.5 Solving Oblique Triangles: Law of Cosines 509

15.1 Bar Graphs 52015.2 Circle Graphs 52315.3 Line Graphs 52615.4 Other Graphs 529

12

13

14

15

Trang 9

15.5 Mean Measurement 53015.6 Other Average Measurements and Percentiles 53215.7 Range and Standard Deviation 535

15.8 Grouped Data 53715.9 Standard Deviation for Grouped Data 54415.10 Statistical Process Control 546

15.11 Other Graphs for Statistical Data 55015.12 Normal Distribution 553

15.13 Probability 55615.14 Independent Events 558

16.1 Introduction to Binary Numbers 56616.2 Addition of Binary Numbers 56816.3 Subtraction of Binary Numbers 56916.4 Multiplication of Binary Numbers 57116.5 Conversion from Decimal to Binary System 57216.6 Conversion from Binary to Decimal System 57316.7 Hexadecimal System 574

16.8 Addition and Subtraction of Hexadecimal Numbers 57616.9 Binary to Hexadecimal Conversion 579

16.10 Hexadecimal Code for Colors 581

Trang 10

Pesticide spraying, 51, 74Profit on feeder cattle, 74Soil nutrient depletion, 288Total yield per acre, 10,288

Tractor depreciation, 9Tractor purchase, 97Volume of bin, 429Volume of wagon box, 429

Volume of cotton bales, 10,51

Weight of dry hay, 104Weight of grain, 283Weight of hay bales, 10Weight of a hog, 289Weight of protein, 85Yield per acre of corn, 51,

195, 283Yield per acre of oats, 10Yield per acre of soybeans,10

Allied Health

Alcohol content ofmedication, 51Calculating dosages, 10,

51, 52, 74, 85, 283, 288Calculating a patient’sinput and output, 9Floor space per hospitalbed, 408

Fluid intake, 9Intravenous (IV), 283, 352Medication vials, 283, 352

Mixing saline solution, 352Potassium solution, 289Preparing medication, 289Storeroom capacity, 408X-ray film, 408

Aviation

Area/size of a runway/

taxiway, 17, 422, 475Area of a militaryoperating zone, 17, 408Area of airspeed indicator,427

Baggage volume, 192Cost of fuel, 73Difference of fuel used, 42Dimensions of wing, 384Distance flown, 9Distance from base airport,480

Flight distance, 74Flight time, 9, 19, 52, 63,

83, 352Fuel used, 42, 195, 288IFR (instrument flightrules), 84

Lateral surface area ofairplane nose, 451Length of side of hexagon-shaped landing pad, 422Length of taxiway, 475Percent of rental time, 84Plane height, 9, 55Plane rental, 84Remaining fuel, 42, 173Search time, 50

Speed of plane, 50, 73Surface area of hemispheri-cal cockpit cover, 454

VFR use, 84VOR (very high frequencyomnidirectional range),

408, 418Volume of baggagecompartment, 439

Auto/Diesel Mechanics

Alternator, 283Amount of oil used, 42Amount of time servicing acar, 42, 51, 74

Antifreeze, 193Auto damage, 512Area occupied by anautomobile, 17Area of side of tire, 427Area/size of mirror, 409,422

Area of windshield, 195Car seat dimensions, 512Calculating displacement,

9, 74Capacity of a fuel tank, 56,289

Changing tires, 51Circumference of rim, 427Converting dimensions, 58Cost of labor, 9

Cost of tires, 9, 73Distance driven, 193Fan belt arrangement, 422Fuel consumption, 9, 288Fuel pump, 288

Grinding a valve, 65Horsepower of an engine,

195, 288Labor cost per hour, 9

ix

Trang 11

Piston ring wear, 65

Planning a storage garage,

Time to detail car, 51

Time to replace tires, 51

Tire pressure, 289

Tire tread depth, 63, 104

Volume of air filter, 444

Conduit across a room, 480

Copper wire resistance, 55

Parts invoice, 89Parallel circuits, 43, 57Percent of overhead, 104Percent of voltage increase,85

Power of circuit, 74Reactance, 417Resistors, 283, 352Spacing of outlets, 51Total current, 417Transformer turns, 283Voltage, 64

Voltage drop, 283, 288,

417, 481Voltage of an iron, 51Voltage in a transformer,283

Wattage, 51, 74Wire length, 51, 288, 352Wiring a shed, 55

Construction

Angles in a roof, 512Area of an opening, 409Blocks needed for wall, 10Boiler placement, 428Brick for wall, 28Buying drywall, 17Buying paint, 18Cable, 73Calculating amounts ofmaterials, 288, 352Calculating amps, 352Calculating board feet oflumber, 50

Calculating materialsneeded, 439Ceiling tiles, 17, 351Concrete mix, 283, 289Concrete pad volume, 51Conduit through abuilding, 416Converting dimensions, 55

Cost of excavation, 73Cost of paint, 409

Cost per square foot of ahouse, 283, 285Diameter of a pipe, 50Difference of ends of taper,65

Distance between centers,

50, 416Distance between rivets, 50Dry wall needed, 18Finding the number ofstuds, 9

Floor space, 73, 85Guy wires length, 480Height of a building, 483Height of door, 55Invoice for a home shell,86

Laying bricks, 409Length of braces, 416, 421Length of cylinder, 23Length of a ladder, 417Length of rafters, 416Length of steel, 50, 440Lumber, 9

Materials needed for aroof, 409

Missing dimensions, 50,

51, 384, 385Mixing concrete, 283Offset of a pipe, 416Pitch of a roof, 288Placement of house, 44Positioning a window, 10Reducing shaft, 44Replacement cost of abuilding, 17Spacing of vents, 51Tap drill size, 44Thickness of plate, 44Tiling a wall, 17Time of bricklayers, 351Time of pump operation,351

Truckload capacity, 351Truckloads of gravel, 451Volume of a concrete pad,51

Volume of cylindrical tank,444

Wall area, 283Wall of pipe thickness, 65

Weight of cement floor, 19Weight of circular tank,451

Industry

Angle of inclination, 480Bolting metal, 192Bracket for a satellite, 428Capacity of spherical watertank, 454

Checking dovetaildimensions, 482Clamping metal, 192Conveyer angle, 479Crankshaft journal, 481Cutting a keyway, 416Diameter of float, 454Design of hopper, 452Distance between holes,416

Hydraulic pressureincrease, 85Lathe operation, 51, 444Length of socket, 65Machinist pay, 85Making holes in metal, 480

Manufacturing cans, 445Measuring metal objects,195

Milling round stock, 416Panels needed for ceiling,409

Perimeter and area of field,428

Pulleys and gears, 428Punching metal, 418Strapping a pipe, 428Tank for liquefiedpetroleum, 455Tapered stock, 452Volume of cylindrical rod,444

Volume of a mold, 440,445

Volume of a tank, 444, 481

Water left in tank, 455Weight of metal stock, 440Weight of steel plate, 74Width of river, 480

Trang 12

Distance between holes, 43

Drying booth length, 289

Finding diameter of shaft,

Tires that are defective, 84

Volume of trash can, 453

Welding

Amount of argon used, 9

Area of metal to form a

container, 17

Area of sheet metal, 56Circular hole, 427Converting dimensions, 55

Cutting a beam, 73Cutting flat steel, 63Cutting pipe, 53Diameter of welding rods,42

Difference in size ofwelding rods, 42Dimensions of metal sheet,384

Dimensions of trapezoidalmetal pieces, 408Distance betweenunwelded ends, 418Gusset dimensions/area/

volume, 418, 422, 433Length of side ofpentagonal piece of flatsteel, 422

Length of support forconveyor belt, 479Lid for circular tank, 427Number/percentage ofwelds, 84

Ratio of steel angle used,283

Ratio of welding rods used,283

Total surface area ofcylindrical storage tank, 444

Total weight of scrapmetal, 173Volume of baggagecompartment, 452Volume of hemisphericalpan, 454

Volume of steel pyramid,451

Volume of tank, 19Welding length, 9, 41, 50,

56, 63, 512Welding production, 352Welding rod cost, 288Welding rods used, 195Welding steel angle, 73,

192, 512Welding time, 351

Technical Career Information

Agriculture supportspecialists, 357Aircraft mechanics andservice technicians, 375Allied health care

professionals, 139Automotive collision repairtechnician, 465

Automotive servicetechnician, 1Computer supportspecialist, 333Construction trades, 219Diesel technician, 243Drafter, 303

Electronics technician, 107Firefighter, 519

Heating, ventilation, conditioning, and refrig-eration technician, 274Manufacturing technologyspecialist, 397

air-Science technician, 165Surveying technicians, 489TelecommunicationsTechnician, 565

CAD/Drafting

Add bay window, 439Air volume of a room, 439,440

Area of shopping center, 19Calculating difference ofoutput, 9

Capacity of septic tank, 56Converting dimensions, 56Cutting small bars, 52Design a box container, 19,440

Design a dome house, 455Design a mating part withpins, 483

Design a swimming pool,441

Design a void in a concretecolumn, 445

Design a void in a concretecube, 440

Diameter of a shaft, 43

Dimensions of building, 353Dimensions of door, 384Dimensions of plot, 353Dimensions of room, 353Dimensions of triangularpedestal, 440

Dimensions of walkway,353

Drilling holes in steel, 44,427

Eave angle, 480Finding a benchmark, 483Finding number of pieces,52

Gallons of water in tank,445

Height of cylindrical tank,444

Internal dimensions of atube, 64

Length of pipe assembly,52

Liquid level in a tank, 85Locating parts, 483Locating windows on awall, 84

Missing dimensions, 42,

43, 52Output difference, 10Perimeter of rectangularcross section, 408Precision drawingdimensions, 193Scupper in pool, 441Slope of bridgeembankment, 84Stair risers, 73Volume of peanuts needed,19

Volume/weight of steelplate, 440, 412Walkway height, 84Weight of a box container,42

HVAC

Air conditioner percent ofmoisture removed, 84Air flow, 56, 84, 193, 352Amount of gas used, 193Cooling requirements, 42

Trang 13

Heater filter size, 422

Lateral surface area of

Volume of furnace filter, 19

Volume of house duct, 19

Biltmore stick, 56Cost of vinyl liner, 441Cost of volume of wood,19

Cost of wood burned, 45

CO2level in 2100, 196Cubic miles of water inlake, 196

Deer density, 86Designing a hot airballoon, 455Dimensions of forest plot,385

Dimensions of full canal,410

Dimensions of lawn, 386Distance a hiker walked,419

Distance kite from person,314

Gallons of plaster to fill:

Triangular pyramid, 453 Right circular cone, 453Grain mixture, 353Height of cliff, 423

Height of falls, 353Increase in humanpopulation, 65Lean-to roofline, 484Length allowing for a kerf,52

Length and slope of sidewalk, 419Length of boards, 353Length of lumber for cat-scratching post, 423Mounting a solar panel,484

MSW decrease, 86MSW for US in 2008, 75Number of firewoodpieces, 52Number of Red/Whiteplants, 52

Percent of catch that wasfilet, 85

Percent of food scraps inlandfill, 196

Pounds of fish sold, 56Recycled materials, 193Salt in seawater, 289Sewage tank volume, 19Size of prey for snake, 514

Storage capacity of silo, 75Storm water runoff, 195Survival rate of mallards,85

Trail length, 45Turns of reel, 289Volume of a rick offirewood, 75Volume of grain in silo,446

Volume of oil in Alaskapipeline, 446Volume of sediment inwastewater plant, 446Volume of water inswimming pool, 441Water use in irrigation, 430Weather balloon volume,455

Weight gain of fish, 283Weight of firewood, 85Weight of fish in cooler,193

Windmill blade travellength and surface area,430

World production of oil in

2007, 455

Trang 14

lementary Technical Mathematics, Tenth Edition, is intended for technical, trade,

al-lied health, or Tech Prep programs This book was written for students who plan tolearn a technical skill, but who have minimal background in mathematics or needconsiderable review To become proficient in most technical programs, students mustlearn basic mathematical skills To that end, Chapters 1 through 4 cover basic arithmeticoperations, fractions, decimals, percent, the metric system, and numbers as measurements.Chapters 5 through 11 present essential algebra needed in technical and trade programs.The essentials of geometry—relationships and formulas for the most common two- andthree-dimensional figures—are given in detail in Chapter 12 Chapters 13 and 14 present

a short but intensive study of trigonometry that includes right-triangle trigonometry aswell as oblique triangles and graphing The concepts of statistics that are most important

to technical fields are discussed in Chapter 15 An introduction to binary and hexadecimalnumbers is found in Chapter 16 for those who requested this material

We have written this text to match the reading level of most technical students Visualimages engage these readers and stimulate the problem-solving process We emphasize thatthese skills are essential for success in technical courses

The following important text features have been retained from previous editions:

• We use a large number of applications from a wide variety of technical areas, cluding auto/diesel mechanics, industrial and construction trades, electronics,agriculture, allied health, CAD/drafting, HVAC, manufacturing, welding, avia-tion, and natural resources

in-• Chapter 1 reviews basic concepts in such a way that individuals, groups of dents, or the entire class can easily study only those sections they need to review

stu-• A comprehensive introduction to basic algebra is presented for those students whoneed it as a prerequisite to more advanced algebra courses However, the book hasbeen written to allow the omission of selected sections or chapters without loss ofcontinuity, to meet the needs of specific students

• More than 6340 exercises assist student learning of skills and concepts

• More than 720 detailed, well-illustrated examples, many with step-by-step ments, support student understanding of skills and concepts

com-E

xiii

Trang 15

• A chapter summary with a glossary of basic terms, a chapter review, and a chaptertest appear at the end of each chapter as aids for students in preparing for quizzesand exams Each chapter test is designed to be completed by an average student in

no more than approximately 50 minutes

1 Give the metric prefix for 1000.

2 Give the metric prefix for 0.01.

3 Which is larger, 200 mg or 1 g?

4 Write the SI unit for the abbreviation 240 ␮L.

5 Write the abbreviation for 30 hectograms.

21 What is the basic SI unit of time?

Fill in each blank:

23 280 W⫽ kW

24 13.9 mA⫽ A

25 720 ps ⫽ ns

26 What is the basic SI unit for temperature?

27 What is the freezing temperature of water on the

Give the metric prefix for each value:

Choose the most reasonable quantity:

35 Jorge and Maria drive a 1600 cm, b 470 m,

c 12 km, or d 2400 mm to college each day.

Trang 16

• The use of a scientific calculator has been integrated in an easy-to-use format withcalculator flowcharts and displays throughout the text to reflect its nearly univer-sal use in technical classes and on the job The instructor should inform the stu-

dents when not to use a calculator.

1 Find the prime factorization of 696.

2 Change 0.081 to a percent.

3 Write 3.015 ⫻ 10 ⫺4in decimal form.

4 Write 28,500 in scientific notation.

9 Read the measurement shown on the vernier caliper in

Illustration 1 a in metric units and b in U.S units.

Example 16

6*41

2=123 4

7,8 =24 35

• Cumulative reviews are provided at the end of every even-numbered chapter tohelp students review for comprehensive exams

Trang 17

• Studies show that current students will experience several career changes duringtheir working lives The chapter-opening pages illustrate various career paths for students to consider as their careers, technology, and the workplace evolve.The basic information provided in the chapter openers about a technical career

is explored in further detail on the Brooks/Cole book companion website atwww.cengage.com/mathematics/ewen

33 A car uses gas at the rate of 31 miles per gallon (mi/gal

or mpg) and has a 16-gallon tank How far can it travel

on one tank of gas?

34 A car uses gas at a rate of 12 kilometres per litre (km/L)

and has a 65-litre tank How far can it travel on one tank

of gas?

35 A four-cylinder engine has a total displacement of

1300 cm 3 Find the displacement of each piston.

36 A car travels 1274 mi and uses 49 gal of gasoline Find

its mileage in miles per gallon.

37 A car travels 2340 km and uses 180 L of gasoline Find

its gas consumption in kilometres per litre.

38 To replace some damaged ductwork, 20 linear feet of

8-in ⫻ 16-in duct is needed The cost is $13 per 4

lin-ear feet What is the cost of replacement?

39 h bill f i i i d h l

ILLUSTRATION 1

16 A pipe 24 ft long is cut into four pieces: the first 4 ft

long, the second 5 ft long, and the third 7 ft long What

is the length of the remaining piece? (Assume no waste from cutting.)

17 A welder needs to weld together pipes of lengths 10 ft,

15 ft, and 14 ft What is the total length of the new pipe?

18 A welder ordered a 125-ft3 cylinder of argon gas, a shielding gas for TIG welding After a few days, only

78 ft 3 remained How much argon was used?

15 Approximately how many studs are needed for the

ex-terior walls in the building shown in Illustration 1? (See Example 4.)

The nation’s construction industry depends on a

technical and competent workforce This workforce includes, but is not limited to, carpenters who cut, fit, and assemble wood and other materials in construction projects; plumbers, pipefitters, and steamfitters who install, maintain, and repair many different types of pipe systems that carry water, steam, air, and other liquids; painters who apply paint, stain, varnish, and other finishes to buildings and other structures; electricians who install, maintain, and repair electrical wiring, equipment, and fixtures; bricklayers and stonemasons who build walls and other structures with bricks, blocks, stones, and other masonry materials;

and structural and reinforcing metal workers who use materials made from iron, steel, and other materials to construct highways, bridges, buildings, and towers.

Construction trade workers often learn their own trade through apprenticeship programs administered by local joint union–management committees or through community college or trade school programs, some of which are offered in partnership with the local joint union–management committees For more information,

go to the website listed below.

Trang 18

Preface xvii

1. Mathematics is used in a variety of places One location where mathematics is used frequently is in the medical profession In small groups, brainstorm about the places in a hospital where you think math is used Think

of the different departments and the different sions in the hospital such as radiology, general surgery, etc After you have thought about this, divide and go to

profes-a hospitprofes-al to check your theory of where profes-and how mprofes-ath

is used Get permission from the proper authorities to ask the employees how they use math One example is pediatricians who use math in prescribing medication

to children They must be careful to get the weight of a child and use this information to prescribe the proper dosage The prescription notifies the pharmacist of the amount of medication to give the patient Make a report

on your findings of how math is used in the medical

field and make special note of the conversions that tors and nurses must use Plan a similar activity for another workplace/profession.

doc-2. Do the following:

a Write how old you are to the day Convert this to

days Convert this to hours and then to minutes.

b Write how tall you are Convert this to feet, to yards,

to inches, to metres, and to centimetres.

c Write how much you weigh Convert this to

kilo-grams and to kilo-grams.

Do a little research and see what gravity is on earth and how your weight is determined by gravity Further research what gravity is on the moon and how your weight would differ on the moon compared to on earth.

(W ⫽ mg)

Chapter 3 Group Activities

• An instructor’s edition that includes all the answers to exercises is available

Significant changes in the tenth edition include the following:

• The following topics were added by special requests of users:

• New category of natural resources application exercises that includes forestry, soil

management, wildlife management, parks, recycling, and related areas

• New Section 1.16, Applications Involving Percent: Personal Finance

• New Section 15.9, Standard Deviation for Grouped Data, and other changes/

updates in Chapter 15

• New Appendix B Exponential Equations

• Signed number drill exercises have been added to assist students to learn addition,subtraction, and multiplication of signed numbers

• More than 330 new exercises have been added

• Chapter objectives have been added

Useful ancillaries available to qualified adopters of this text include the following:

• Instructor’s Edition The Instructor’s Edition features an appendix containing the

answers to all problems in the book (1-4390-4724-3)

• PowerLecture™ CD-ROM with ExamView ®This CD-ROM provides dynamicmedia tools for teaching Create, deliver, and customize tests (both print and on-line) in minutes with ExamView®Computerized Testing Featuring AlgorithmicEquations Easily build solution sets for homework or exams using SolutionBuilder’s online solutions manual Microsoft®PowerPoint®lecture slides, figuresfrom the book, and a Test Bank, in electronic format, are also included

(1-4390-4752-9)

• Solutions Builder Easily build solution sets for homework or exams using

Solu-tion Builder’s online soluSolu-tions manual (1-4390-4753-7)

• Group activity projects are included at the end of each chapter

Trang 19

• WebAssign WebAssign, the most widely used homework system in higher

educa-tion, allows you to assign, collect, grade, and record homework assignments viathe Web Through a partnership between WebAssign and Cengage LearningBrooks/Cole, this proven homework system has been enhanced to include links to textbook sections, video examples, and problem-specific tutorials (0-538-73899-5)

We are grateful for the courtesy of the L S Starrett Company in allowing us to usephotographs of their instruments in Chapter 4 The authors also thank the many facultymembers who used earlier editions and who offered suggestions In particular, we thankWilliam G Camp, Professor, Cornell University and Professor Emeritus, Virginia Tech andMartin Alderman, Cornell University PhysTEC Teacher in Residence for writing natural re-sources applications problems and the following reviewers: Amir F Arabi, Central VirginiaCommunity College; Cynthia Broughton, Arizona Western College; Nancy Jo Buchli,Southeast Community College–Milford; James Carpenter, College of the Mainland; AmyCurry, College of Lake County; Royetta S Ealba, Henry Ford Community College;Jonathan Greer, Grand Rapids Community College; Mehran Hassanpour, South TexasCommunity College; Paul McCombs, Rock Valley College; Gray McCracken, SheltonState Community College; Lorie McFee, North Buncomble High School; Carol McVey,Florence-Darlington Technical College; Lara Michaels, Green River Community College;Linda Nokes, Southwestern Michigan College; Arthur M Peck, Lane Community College;Catherine Pellish, Front Range Community College; Gary Rattray, Central Maine Commu-nity Collge; Fran Seigle, Lakes Region Community College; Richard Watikins, TidewaterCommunity College; Emily E White, Enka High School; and Carol L Williams, Des MoinesArea Community College

Anyone wishing to correspond regarding suggestions or questions should write DaleEwen through the publisher

For all their help, we thank our editor, Marc Bove; assistant editor, Stefanie Beeck; andthe staff of Cengage Learning Brooks/Cole We also greatly appreciate the diligent, per-sonal, and professional efforts of Lynn Steines, S4Carlisle Publishing Services, in coordi-nating production; Lorretta Palagi for a great job copy editing; Curtis Nunn for checkingthe answers; and Brian Morris of Scientific Illustrators for the outstanding artwork

Dale Ewen

C Robert Nelson

Trang 20

Basic Concepts

www.cengage.com/mathematics/ewen

1

Mathematics at Work

A utomotive service technicians inspect, maintain,

and repair automobiles, light trucks, and vans In

the past, these workers were called mechanics.

The increasing sophistication of automotive technology

now requires workers to be able to use computerized

shop equipment and work with electronic components

in addition to the traditional hand tools When a

mechanical or electronic problem occurs, the technician

uses a diagnostic approach to repair the problem based

on information from the owner and the information

obtained from the service equipment and computerized

databases and service manuals.

The National Automotive Technicians Education

Foundation (NATEF), an affiliate of the National Institute

for Automotive Service Excellence (ASE), certifies

automotive service technician, collision repair and

refinish technician, engine specialist, and medium/heavy

truck technician training programs offered by community

colleges, postsecondary trade schools, technical

institutes, and high schools Although voluntary, NATEF

certification signifies that the program meets uniform

standards for instructional facilities, equipment, staff

credentials, and curriculum Various automobile

manufacturers and their participating dealers also

sponsor two-year associate degree programs at

postsecondary schools across the United States

For more information, go to the website listed below.

Automotive Service Technician

Automotive service technician working on anautomobile

1

Trang 21

■ Add, subtract, multiply, and divide whole numbers.

■ Add, subtract, multiply, and divide whole numbers with a scientificcalculator

■ Apply the rules for order of operations

■ Find the area and volume of geometric figures

■ Evaluate formulas

■ Find the prime factorization of whole numbers

■ Add, subtract, multiply, and divide fractions

■ Add, subtract, multiply, and divide fractions with a scientific calculator

■ Use conversion factors to change from one unit to another within theU.S system of weights and measures

■ Add, subtract, multiply, and divide decimal fractions

■ Add, subtract, multiply, and divide decimal fractions with a scientificcalculator

■ Round numbers to a particular place value

■ Apply the percent concept; change a percent to a decimal, a decimal to

a percent, a fraction to a percent, and a percent to a fraction

■ Solve application problems involving the addition, subtraction,multiplication, and division of whole numbers, fractions, and decimalfractions and percents

■ Find powers and roots of numbers using a scientific calculator

■ Solve personal finance problems involving percent

Objectives

Unit 1A

REVIEW OF OPERATIONS WITH WHOLE NUMBERS

The positive integers are the numbers 1, 2, 3, 4, 5, 6, and so on They can also be written

as 1, 2, 3, and so on, but usually the positive () sign is omitted The whole

num-bers are the numnum-bers 0, 1, 2, 3, 4, 5, 6, and so on That is, the whole numnum-bers consist of the

positive integers and zero

The value of any digit in a number is determined by its place in the particular number.Each place represents a certain power of ten By powers of ten, we mean the following:

100 1

101 10

Trang 22

1.1 ■ Review of Basic Operations 3

102 10 10 100 (the second power of 10)

103 10 10 10 1000 (the third power of 10)

104 10 10 10 10 10,000 (the fourth power of 10) and so on

Note: A small superscript number (such as the 2 in 102) is called an exponent.

The number 2354 means 2 thousands plus 3 hundreds plus 5 tens plus 4 ones

In the number 236,895,174, each digit has been multiplied by some power of 10, asshown below

Add: 238 15 9 3564

238159

Subtraction is the inverse operation of addition Therefore, subtraction can be thought

of in terms of addition The “” (minus) sign is the symbol for subtraction The quantity

5 3 can be thought of as “what number added to 3 gives 5?” The result of subtraction is

called the difference.

To check a subtraction, add the difference to the second number If the sum is equal tothe first number, the subtraction has been done correctly

2843 This sum equals the first number, so

The “” (plus) symbol is the sign for addition, as in the expression 5 7 The result of

adding the numbers (in this case, 12) is called the sum Integers are added in columns with the

digits representing like powers of ten in the same vertical line (Vertical means up and down.)

Trang 23

Switch Load

The light bulb may be represented as a resistance Then the circuit diagram in Figure 1.1bwould appear as in Figure 1.2, where

represents the resistorrepresents the switchrepresents the source The short line represents the negativeterminal of a battery, and the long line represents the positiveterminal The current flows from negative to positive

There are two basic types of electrical circuits: series and parallel An electrical

cir-cuit with only one path for the current, I, to flow is called a series circir-cuit (Figure 1.3a) An electrical circuit with more than one path for the current to flow is called a parallel circuit

(Figure 1.3b) A circuit breaker or fuse in a house is wired in series with its outlets Theoutlets themselves are wired in parallel

Trang 24

insu-is shown in Figure 1.5.) Studs are normally placed 16 in on center and are placed double

at all internal and external corners of a building The number of studs needed in a wall can

be estimated by finding the number of linear feet (ft) of the wall How many studs areneeded for the exterior walls of the building in Figure 1.6?

Trang 25

Repeated addition of the same number can be shortened by multiplication The “”

(times) and the “#” (raised dot) are used to indicate multiplication When adding the lengths

of five pipes, each 7 ft long, we have 7 ft 7 ft 7 ft 7 ft 7 ft 35 ft of pipe In

mul-tiplication, this would be 5 7 ft 35 ft The 5 and 7 are called factors The result of

mul-tiplying numbers (in this case, 35) is called the product Computing areas, volumes, forces,

and distances requires skills in multiplication

Multiply: 358 18

3582864

Division is the inverse operation of multiplication The following symbols are used to

show division: 15 5, , 15/5, and The quantity 15 5 can also be thought of as

“what number times 5 gives 15?” The answer to this question is 3, which is 15 divided by

5 The result of dividing numbers (in this case, 3) is called the quotient The number to be

divided, 15, is called the dividend The number you divide by, 5, is called the divisor.

15 55冷15

The remainder (when not 0) is usually written in one of two ways: with an “r”

preced-ing it or with the remainder written over the divisor as a fraction, as shown in Example 8.(Fractions are discussed in Unit 1B.)

42

7c7冷11516

Trang 26

An 8-row corn planter costs $50,400 It has a 10-year life and a salvage value of $5000.What is the annual depreciation? (Use the straight-line depreciation method.)

The straight-line depreciation method means that the difference between the cost andthe salvage value is divided evenly over the life of the item In this case, the difference be-tween the cost and the salvage value is

Using a Scientific Calculator

Use of a scientific calculator is integrated throughout this text To demonstrate how to use

a common scientific calculator, we show which keys to use and the order in which they arepushed We have chosen to illustrate the most common types of algebraic logic calculators.Yours may differ If so, consult your manual

Note: We will always assume that your calculator is cleared before you begin any

calculation

Use a calculator to add, subtract, multiply, and divide as shown in the following examples

9677

Add: 9463

1259

80

Example 11

Trang 27

The quotient is 580 ■

Note: Your instructor will indicate which exercises should be completed using a calculator.

1872

8500

580

Find the total resistance in each series circuit:

Trang 28

33 A car uses gas at the rate of 31 miles per gallon (mi/gal

or mpg) and has a 16-gallon tank How far can it travel

on one tank of gas?

34 A car uses gas at a rate of 12 kilometres per litre (km/L)

and has a 65-litre tank How far can it travel on one tank

of gas?

35 A four-cylinder engine has a total displacement of

1300 cm3 Find the displacement of each piston

36 A car travels 1274 mi and uses 49 gal of gasoline Find

its mileage in miles per gallon

37 A car travels 2340 km and uses 180 L of gasoline Find

its gas consumption in kilometres per litre

38 To replace some damaged ductwork, 20 linear feet of

8-in 16-in duct is needed The cost is $13 per 4

lin-ear feet What is the cost of replacement?

39 The bill for a new transmission was received The total

cost for labor was $402 If the car was serviced for 6 h,find the cost of labor per hour

40 The cost for a set of four Pirelli P4000 Super-touring

tires of size 215/70ZR15 is $508 What is the price for

each tire?

41 A small Cessna aircraft has enough fuel to fly for 4 h.

If the aircraft cruises at a ground speed of 125 milesper hour (mi/h or mph), how many miles can the air-craft fly in the 4 h?

42 A small plane takes off and climbs at a rate of 500 ft/min.

If the plane levels off after 15 min, how high is the plane?

43 Inventory shows the following lengths of 3-inch steel

ILLUSTRATION 1

16 A pipe 24 ft long is cut into four pieces: the first 4 ft

long, the second 5 ft long, and the third 7 ft long What

is the length of the remaining piece? (Assume no waste

from cutting.)

17 A welder needs to weld together pipes of lengths 10 ft,

15 ft, and 14 ft What is the total length of the new pipe?

18 A welder ordered a 125-ft3 cylinder of argon gas, a

shielding gas for TIG welding After a few days, only

78 ft3remained How much argon was used?

19 Total the following input and output (I-O) entries in

cubic centimetres (cm3)* for a patient

Input: 300 cm3, 550 cm3, 150 cm3, 75 cm3,

150 cm3, 450 cm3, 250 cm3

Output: 325 cm3, 150 cm3, 525 cm3, 250 cm3,

175 cm3

20 A student pilot must complete 40 h of total flight time

as required for her private pilot certificate She had

al-ready entered 31 h of flight time in her logbook

Mon-day she logged another 2 h, then WednesMon-day she logged

another 3 h, and Friday she logged yet another 2 h If

she can fly 3 h more on Saturday, will she have enough

total time as required for the certificate?

Multiply:

15 Approximately how many studs are needed for the

ex-terior walls in the building shown in Illustration 1? (See

used throughout this book, some readers may be more familiar

with the abbreviation “cc,” which is still used in some medical

and allied health areas.

44 An order of lumber contains 36 boards 12 ft long,

28 boards 10 ft long, 36 boards 8 ft long, and 12 boards

16 ft long How many boards are contained in the order?How many linear feet of lumber are contained in the order?

Trang 29

45 Two draftpersons operating the same computer plotter

work 8 hours each, on a day and night shift basis One

produces 80 drawings per hour; the other produces

120 drawings per hour What is the difference in their

outputs after 30 days?

46 A shipment contains a total of 5232 linear feet of steel

pipe Each piece of pipe is 12 ft long How many pieces

should be expected?

47 How should a window 75 in wide be placed so that it

is centered on a wall 17 ft 5 in wide?

48 A farmer expects a yield of 165 bushels per acre

(bu/acre) from 260 acres of corn If the corn is stored,

how many bushels of storage are needed?

49 A farmer harvests 6864 bushels (bu) of soybeans from

156 acres What is his yield per acre?

50 A railroad freight car can hold 2035 bu of corn How

many freight cars are needed to haul the expected

12,000,000 bu from a local grain elevator?

51 On a given day, eight steers weighed 856 lb, 754 lb,

1044 lb, 928 lb, 888 lb, 734 lb, 953 lb, and 891 lb

a What is the average weight? b In 36 days, 4320 lb of

feed is consumed What is the average feed

consump-tion per day per steer?

52 What is the weight (in tons) of a stack of hay bales

6 bales wide, 110 bales long, and 15 bales high? The

av-erage weight of each bale is 80 lb (1 ton ⫽ 2000 lb.)

53 From a 34-acre field, 92,480 lb of oats are harvested.

Find the yield in bushels per acre (1 bu of oats weighs

32 lb.)

54 A standard bale of cotton weighs approximately 500 lb.

How many bales are contained in 15 tons of cotton?

55 A tractor costs $175,000 It has a 10-year life and a

sal-vage value of $3000 What is the annual depreciation?

(Use the straight-line depreciation method See

Exam-ple 10.)

56 How much pesticide powder would you put in a

400-gal spray tank if 10 gal of spray, containing 2 lb of

pesticide, are applied per acre?

Using Ohm’s law, find the current I in amps (A) in each

electrical circuit (see Example 9):

61 A hospital dietitian determines that each patient needs

4 ounces (oz) of orange juice How many ounces of ange juice must be prepared for 220 patients?

or-62 During 24 hours, a patient is given three phenobarbital

tablets of 60 mg each How many milligrams of barbital does the patient receive altogether?

pheno-63 To give 800 mg of quinine sulfate from 200-mg tablets,

how many tablets would you use?

64 A nurse used two 4-grain potassium permanganate

tablets in the preparation of a medication How muchpotassium permanganate did she use?

65 A sun room addition to a home has a wall 14 ft 6 in long

measured from inside wall to inside wall Four dows are to be equally spaced from each other in thiswall The windows are 2 ft 6 in wide including the in-side window molding What is the space between thewall and windows shown in Illustration 2?

win-ILLUSTRATION 2

14 ft 6 in.

66 A solid concrete block wall is being built around a

rec-tangular storage building 12 ft 8 in by 17 ft 4 in using16-in.-long by 8-in.-high by 4-in.-thick concrete block.How many blocks will be needed to build the 8-ft-highwall around the building as shown in Illustration 3? (Ignore the mortar joints.)

Trang 30

1.2 ■ Order of Operations 11

8 ft

ILLUSTRATION 3

67 A sheet of plywood 8 ft long is painted with three

equally spaced stripes to mark off a hazardous area as

shown in Illustration 4 If each stripe is 10 in wide,

what is the space between the end of the plywood and

the first stripe?

8 ft

ILLUSTRATION 4

68 In a small machine shop, eight 5-gallon drums of oil are

on hand If 2 gallons are used each day and the ownerwants a 30-day supply on hand, how many drumsshould be ordered?

69 Using a process called “cruising timber,” foresters can

estimate the amount of lumber in board feet in trees fore they are cut down In a stand of 1000 trees, aforester selects a representative sample of 100 trees andestimates that the sample contains 8540 board feet oflumber If the entire stand containing 2500 trees is har-vested, how many board feet would the landowner ex-pect to harvest?

be-70 In tilapia aquaculture production, a feed conversion

ra-tio of 2 lb of high-protein pelleted feed per pound ofweight gain, after death losses, is not unusual At thatrate of feed conversion, if fish food costs $520 per ton(2000 lb), what would be the feed cost per pound of livefish produced?

The expression 53means to use 5 as a factor 3 times We say that 53is the third power of 5, where 5 is called the base and 3 is called the exponent Here, 53means 5 ⫻ 5 ⫻ 5 ⫽ 125

The expression 24means that 2 is used as a factor 4 times; that is, 24⫽ 2 ⫻ 2 ⫻ 2 ⫻ 2 ⫽

16 Here, 24is the fourth power of 2

Just as we use periods, commas, and other punctuation marks to help make sentences

more readable, we use grouping symbols in mathematics, such as parentheses “( )” and

brackets “[ ],” to help clarify the meaning of mathematical expressions Parentheses not

only give an expression a particular meaning, they also specify the order to be followed inevaluating and simplifying expressions

What is the value of 8 ⫺ 3 #2? Is it 10? Is it 2? Or is it some other number? It is veryimportant that each mathematical expression have only one value For this to happen, we

all must not only perform the exact same operations in a given mathematical expression or problem but also perform them in exactly the same order The following order of opera-

tions is followed by all

Trang 31

Order of Operations

1 Always do the operations within parentheses or other grouping symbols first.

2 Then evaluate each power, if any Examples:

4 32 4 (3 3) 4 9 36

52 6 (5 5) 6 25 6 150

3 Next, perform multiplications and divisions in the order in which they appear as

you read from left to right For example,

4 Finally, perform additions and subtractions in the order in which they appear as

you read from left to right

Note: If two parentheses or a number and a parenthesis occur next to one another

without any sign between them, multiplication is indicated

Evaluate: 2 5(7 6)

2 5(13) Add within parentheses.

2 65 Multiply.

Note: A number next to parentheses indicates multiplication In Example 1, 5(13) means

5 13 Adjacent parentheses also indicate multiplication: (5)(13) also means 5 13 ■

Trang 32

1.2 ■ Order of Operations 13

Evaluate: 4(16 4) 8

Subtract within parentheses.

48 2 8 Multiply and divide.

= 4( 12 ) + 14

7 - 8

147

Example 4

Evaluate: 7 (6 2)2

7 42 Subtract within parentheses.

7 16 Evaluate the power.

Trang 33

1.3 Area and Volume

To measure the length of an object, you must first select a suitable standard unit of length

To measure short lengths, choose a unit such as centimetres or millimetres in the metric tem, or inches in the U.S or, as it is still sometimes called, the English system For long dis-tances, choose metres or kilometres in the metric system, or yards or miles in the U.S.system

sys-Area

The area of a plane geometric figure is the number of square units of measure it contains.

To measure the surface area of an object, first select a standard unit of area suitable to theobject to be measured Standard units of area are based on the square and are called squareunits For example, a square inch (in2) is the amount of surface area within a square thatmeasures one inch on a side A square centimetre (cm2) is the amount of surface area within

a square that is 1 cm on a side (See Figure 1.8.)

Trang 34

1.3 ■ Area and Volume 15

What is the area of a rectangle measuring 4 cm by 3 cm?

Each square in Figure 1.9 represents 1 cm2 By simply counting the number of squares,you find that the area of the rectangle is 12 cm2

You can also find the area by multiplying the length times the width:

What is the area of the metal plate represented in Figure 1.10?

Each square represents 1 square inch By simply counting the number of squares, wefind that the area of the metal plate is 42 in2

Another way to find the area of the figure is to find the areas of two rectangles and thenfind their difference, as in Figure 1.11

Area of outer rectangle: 9 in 8 in 72 in2

Area of inner rectangle: 5 in 6 in

Area of metal plate: 42 in2 Subtract. ■

30 in2

Volume

The volume of a solid geometric figure is the number of cubic units of measure it contains.

In area measurement, the standard units are based on the square and called square units Forvolume measurement, the standard units are based on the cube and called cubic units Forexample, a cubic inch (in3) is the amount of space contained in a cube that measures 1 in

on each edge A cubic centimetre (cm3) is the amount of space contained in a cube thatmeasures 1 cm on each edge A cubic foot (ft3) is the amount of space contained in a cubethat measures 1 ft (or 12 in.) on each edge (See Figure 1.12.)

Trang 35

Figure 1.13 shows that the cubic decimetre (litre) is made up of 10 layers, each taining 100 cm3, for a total of 1000 cm3.

con-Find the volume of a rectangular box 8 cm long, 4 cm wide, and 6 cm high

Suppose you placed one-centimetre cubes in the box, as in Figure 1.14 On the bottomlayer, there would be 8 4, or 32, one-cm cubes In all, there are six such layers, or

6 32 192 one-cm cubes Therefore, the volume is 192 cm3

.You can also find the volume of a rectangular solid by multiplying the length times thewidth times the height:

How many cubic inches are in one cubic foot?

The bottom layer of Figure 1.15 contains 12 12, or 144, one-inch cubes There are

12 such layers, or 12 144 1728 one-inch cubes Therefore, 1 ft3 1728 in3

Trang 36

1.3 ■ Area and Volume 17

1 How many square yards (yd2) are contained in a

rectan-gle 12 yd long and 8 yd wide?

2 How many square metres (m2) are contained in a

rec-tangle 12 m long and 8 m wide?

3 At a small airport, Runway 11-29 is 4100 ft long and

75 ft wide What is the area of the runway?

4 A small rectangular military operating zone has

dimen-sions 12 mi by 22 mi What is its area?

5 A 2009 Honda Accord LX measures 191 in by 73 in.

Find the area it occupies

6 Five pieces of sheet metal have been cut to form a

con-tainer The five pieces are of sizes 27 by 15, 15 by 18,

27 by 18, 27 by 18, and 15 by 18 (all in inches) What

is the total area of all five pieces?

In the following exercises, assume that all corners are

square and that like measurements are not repeated because

the figures are assumed to have consistent lengths All three

of the following mean that the length of a side is 3 cm:

13 How many tiles 4 in on a side should be used to cover

a portion of a wall 48 in long by 36 in high? (See Illustration 1.)

Trang 37

22.

23.

24.

18 The replacement cost for construction of the building in

Illustration 4 is $90/ft2 Determine how much insurance

should be carried for full replacement

14 How many ceiling tiles 2 ft by 4 ft are needed to tile a

ceiling that is 24 ft by 26 ft? (Be careful how you

arrange the tiles.)

15 How many gallons of paint should be purchased to paint

20 motel rooms as shown in Illustration 2? (Do not paint

the floor.) One gallon is needed to paint 400 square feet

(ft2)

ILLUSTRATION 2

16 How many pieces of 4-ft by 8-ft drywall are needed for

the 20 motel rooms in Exercise 15? All four walls and

the ceiling in each room are to be drywalled Assume

that the drywall cut out for windows and doors cannot

be salvaged and used again

17 The replacement cost for construction of houses is

$110/ft2 Determine how much house insurance should

be carried on each of the one-story houses in

Trang 38

27 Common house duct is 8-in by 20-in rectangular metal

duct If the length of a piece of duct is 72 in., what is its

volume?

28 A furnace filter measures 16 in by 20 in by 1 in What

is its volume?

29 A large rectangular tank is to be made of sheet metal as

follows: 3 ft by 5 ft for the top and the base, two sides

consisting of 2 ft by 3 ft, and two sides consisting of

2 ft by 5 ft Find the volume of this container

30 Suppose an oil pan has the rectangular dimensions 14 in.

by 16 in by 4 in Find its volume

31 Find the weight of a cement floor that is 15 ft by 12 ft

by 2 ft if 1 ft3of cement weighs 193 lb

32 A trailer 5 ft by 6 ft by 5 ft is filled with coal Given that

1 ft3of coal weighs 40 lb and 1 ton 2000 lb, how

many tons of coal are in the trailer?

33 A rectangular tank is 8 ft long by 5 ft wide by 6 ft high.

Water weighs approximately 62 lb/ft3 Find the weight

of water if the tank is full

34 A rectangular tank is 9 ft by 6 ft by 4 ft Gasoline weighs

approximately 42 lb/ft3 Find the weight of gasoline if

the tank is full

35 A building is 100 ft long, 50 ft wide, and 10 ft high.

Estimate the cost of heating it at the rate of $55 per

1000 ft3

36 A single-story shopping center is being designed to be

483 ft long by 90 ft deep Two stores have been

pre-leased One occupies 160 linear feet and the other will

occupy 210 linear feet The owner is trying to decide

how to divide the remaining space, knowing that the

smallest possible space should be 4000 ft2 How many

stores can occupy the remaining area as shown in

Illus-tration 5?

25 Find the volume of a rectangular box 10 cm by 12 cm

by 5 cm

26 A mountain cabin has a single room 20 ft by 10 ft by

8 ft high What is the total volume of air in the room that

will be circulated through the central ventilating fan?

483 ft

90 ft

How many stores?

37 A trophy company needs a shipping box for a trophy

15 in high with an 8-in.-square base The box company

is drawing the die to cut the cardboard for this box.How large a sheet of cardboard is needed to make onebox that allows 1 in for packing and 1 in for a glueedge as shown in Illustration 6?

ILLUSTRATION 6

38 Styrofoam “peanuts” will be used to pack the trophy in

the box in Illustration 6 to prevent the trophy from beingbroken during shipment Ignoring the box wall thickness,how many cubic inches of peanuts will be used for eachpackage if the volume of the trophy is 450 in3?

39 A standard cord of wood measures 4 ft by 4 ft by 8 ft.

What is the volume in cubic feet of a cord of wood?

40 A municipal wastewater treatment plant has a settling

tank that is 125 ft long and 24 ft wide with an effectivedepth of 12 ft What is the surface area of the liquid inthe tank and what is the volume of sewerage that thesettling tank will hold?

A formula is a statement of a rule using letters to represent the relationship of certain

quanti-ties In physics, one of the basic rules states that work equals force times distance If a person

(Figure 1.16) lifts a 200-lb weight a distance of 3 ft, we say the work done is 200 lb 3 ft

600 foot-pounds (ft-lb) The work, W, equals the force, f, times the distance, d, or W f d.

Trang 39

To summarize, if you know the amount of force and the distance the force is applied, the

work can be found by simply multiplying the force and distance The formula W ⫽ f ⫻ d

is often written W ⫽ f # d, or simply W ⫽ fd Whenever there is no symbol between a

number and a letter or between two letters, it is assumed that the operation to be performed ismultiplication

I = ER

A person pushes against a car weighing 2700 lb but does not move it The work done

is 2700 lb ⫻ 0 ft ⫽ 0 ft-lb An automotive technician (Figure 1.17) moves a diesel engine

weighing 1100 lb from the floor to a workbench 4 ft high The work done in moving the gine is 1100 lb ⫻ 4 ft ⫽ 4400 ft-lb

Trang 40

I = ER

Formulas from Geometry

The area of a triangle is given by the formula , where b is the length of the base and h, the height, is the length of the altitude to the base (Figure 1.18) (An altitude of a tri-

angle is a line from a vertex perpendicular to the opposite side.)

tance between the base and its opposite side (Figure 1.19)

Find the area of a parallelogram with base 24 cm and height 10 cm

A bh

A (24 cm)(10 cm)

Example 5

Định dạng
Số trang	651
Dung lượng	14,94 MB